Inclusion Criteria:

- Patients with a histologically confirmed diagnosis of medulloblastoma that is
recurrent, progressive, or refractory to standard therapy and for which there is no
known curative therapy

- Patient has immunohistochemical (IHC) evidence of Hh pathway-activated tumor (stratum
B only)

- Patients must have bi-dimensionally measurable disease in the brain or spinal cord
defined as at least one lesion that can be accurately measured in at least 2 planes
in order to be eligible for this study

- Patients with neurological deficits should have deficits that are stable for a
minimum of 1 week prior to registration

- Patient must have adequate archival formalin-fixed, paraffin-embedded (FFPE) primary
tumor material for biology studies

- No CNS embryonal tumor other than medulloblastoma (patients with diagnosis of
atypical teratoid/rhabdoid tumor (ATRT), PNET from a non-cerebellar site within the
central nervous system, ependymoblastoma, or medulloepithelioma)

- Karnofsky performance status of ≥ 50% in patients > 16 years, or Lansky performance
status of ≥ 50% in patients ≥ 3 yrs and ≤ 16 years

- ANC ≥ 1,000 μL

- Platelet count ≥ 50,000/μL (transfusion independent)

- Hemoglobin ≥ 8.0 g/dL (may receive RBC transfusions)

- Creatinine clearance or radioisotope GFR ≥ 70 mL/min OR a serum creatinine 1.5 mg/dL

- Serum total bilirubin ≤ 1.5 x upper limit of normal (ULN) for age

- ALT ≤ 2.5 x institutional ULN for age

- AST ≤ 2.5 x institutional ULN for age

- Alkaline phosphatase ≤ 1.5 x institutional ULN

- Serum albumin ≥ 2.5 g/dL

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use 2 forms of acceptable contraception, including one barrier
method, during and for 12 months after completion of study treatment

- 100% commitment to abstinence is considered an acceptable form of birth control

- Patients must have a BSA of ≥ 0.67 m^2 and at most 2.5 m^2

- No patients with any clinically significant unrelated systemic illness (serious
infections or significant cardiac, pulmonary, hepatic or other organ dysfunction)that
would compromise the patient's ability to tolerate protocol therapy or would likely
interfere with the study procedures or results

- No patients with inability to return for follow-up visits or obtain follow-up studies
required to assess toxicity to therapy

- None of the following:

- Inability to swallow capsules

- Malabsorption syndrome or other condition that would interfere with enteral
absorption

- History of congestive heart failure

- History of ventricular arrhythmia requiring medication

- Uncontrolled hypocalcemia, hypomagnesemia, hyponatremia, or hypokalemia defined
as less than the lower limit of normal for the institution despite adequate
electrolyte supplementation

- Clinically important history of liver disease, including viral or other
hepatitis or cirrhosis

- Male patients may not donate sperm during or for 12 months after completion of study
treatment

- Female patients may not donate ova while being treated with GDC-0449

- Patients may not donate blood for 12 months after completion of study treatment

- Patient must not be receiving warfarin

- Prior therapy will include primary therapy (including radiation therapy and
chemotherapy) and a maximum of 2 additional salvage therapies

- Patients can enroll on the protocol after failure on primary therapy

- Must have recovered from prior treatment-related toxicity

- No other myelosuppressive chemotherapy or immunotherapy within 4 weeks prior to study
entry (6 weeks if prior nitrosourea)

- Decadron dose should also be stable or decreasing for at least 1 week (7 days) prior
to starting therapy

- Radiotherapy: ≥ 3 months prior to study entry for craniospinal irradiation; ≥ 8 weeks
for local irradiation to primary tumor; ≥ 2 weeks prior to study entry for focal
irradiation for symptomatic metastatic sites

- Off all colony-stimulating factors > 1 week prior to study entry (G-CSF,GM-CSF,
erythropoietin)

- No patients receiving any other anticancer or investigational drug therapy